Corresponding author:
Professor Nick Glozier
Faculty of Medicine and Health,
University of Sydney,
NSW 2050,
Australia
email: nick.glozier@sydney.edu.au
Draft: 08 February, 2021
Supplementary tables: 4
Supplementary figures: 3
keywords: Subjective wellbeing, household wealth, HILDA
The broad demographic characteristics of the sample at each fourth year wave are presented below in Table S1.
Characteristic | 2002 | 2006 | 2010 | 2014 | 2018 |
Life satisfaction | 7.9 (±1.6) | 7.9 (±1.5) | 7.8 (±1.5) | 7.9 (±1.5) | 7.9 (±1.5) |
Happiness | 68.3 (±16.8) | 68.3 (±16.7) | 67.9 (±16.6) | 67.6 (±17.1) | 66.5 (±17.3) |
Sex | |||||
Female | 6,088 (52%) | 6,069 (53%) | 6,296 (52%) | 8,100 (52%) | 8,241 (52%) |
Male | 5,547 (48%) | 5,405 (47%) | 5,697 (48%) | 7,396 (48%) | 7,480 (48%) |
Age (years) | 46.4 (±16.6) | 46.8 (±17.3) | 46.9 (±17.7) | 47.7 (±17.8) | 48.2 (±18.2) |
Education | |||||
High school or less | 9,348 (80%) | 8,943 (78%) | 9,186 (77%) | 11,408 (74%) | 11,268 (72%) |
Graduate | 2,281 (20%) | 2,526 (22%) | 2,800 (23%) | 4,077 (26%) | 4,445 (28%) |
Workforce | |||||
Employed | 7,323 (63%) | 7,568 (66%) | 7,861 (66%) | 9,916 (64%) | 10,141 (65%) |
Unemployed | 389 (3.3%) | 290 (2.5%) | 384 (3.2%) | 550 (3.5%) | 500 (3.2%) |
Not in labour force | 3,923 (34%) | 3,616 (32%) | 3,748 (31%) | 5,030 (32%) | 5,080 (32%) |
Relationship status | |||||
Single | 1,847 (16%) | 1,913 (17%) | 2,063 (17%) | 2,669 (17%) | 2,782 (18%) |
Married | 7,956 (68%) | 7,737 (67%) | 8,106 (68%) | 10,558 (68%) | 10,630 (68%) |
Divorced/Widow | 1,832 (16%) | 1,824 (16%) | 1,824 (15%) | 2,269 (15%) | 2,309 (15%) |
Chronic illness | 2,735 (24%) | 3,278 (29%) | 3,467 (29%) | 4,757 (31%) | 4,849 (31%) |
SEIFA | 5.5 (±2.9) | 5.6 (±2.8) | 5.6 (±2.8) | 5.5 (±2.8) | 5.6 (±2.8) |
Household size | 2.8 (±1.4) | 2.8 (±1.4) | 2.8 (±1.4) | 2.8 (±1.5) | 2.8 (±1.4) |
1Statistics presented: Mean (±SD); n (%) | |||||
Average life satisfaction levels were very steady between 2002-2018, while average happiness score decreased slightly over the 17 years. The proportions of each sex and relationship status were stable over time, as were the average household size and SEIFA index. However age and chronic health conditions tended to increase over time, indicating a slight increase in the age of the panel over time (1.8 years) but not that of a cohort study which would be 16 years. Education levels (i.e., graduate percentage) also tended to increase over time, while changes in the workforce varied with economic circumstances.
We compared the posterior evidence of a linear- over a nonlinear- relationship between each wellbeing variable and income (i.e., WAIClinear — WAICpiecewise). Thus a WAIC difference greater than zero indicated evidence for a linear relationship. A WAIC difference less than zero indicated evidence for a nonlinear (piecewise) relationship.
Figure S1 legend: Differences in posterior evidence for a linear fit over a piecewise fit (WAIC) for happiness (red) and satisfaction (blue). The filled circle indicates the mean of the distribution and the horizontal bars represents the 95% credible interval. A difference greater than zero is support for the linear model and a difference below zero is support for the piecewise model.
The posterior evidence from model selection revealed the nonlinear (piecewise) fit of happiness, but not satisfaction, was credibly superior to a linear fit in each year. Figure S1 shows the 95% credible interval of the difference in WAIC values for the linear over nonlinear fits for happiness was below zero with no overlap for each year, indicating consistent support for the nonlinear model. By contrast, the WAIC differences for the satisfaction models were generally positive, indicating the superiority of the linear fit for this dependent variable. Overall the posterior evidence suggests that happiness and satisfaction have distinct relationships with household income; satisfaction tends to increase linearly with income, while a change point exists in the relationship between happiness and household income.
The posterior estimates of the piecewise model indicated that the relationship between happiness and income changed over time between 2002 and 2018. One implication of such a change is the disparity in happiness between income groups has increased. This will occur as more people fall below the change point over time and so are subject to the steep region of the function where income and happiness are strongly related. To directly examine the implications of our model for such inequities in happiness, we used the model to estimate or predict the happiness of two different income levels: one income level which fell below the change points between 2002-2018 ($40K/yr); and another level which always remained above the change points over the same period ($75K/yr). Figure S2 below presents the happiness levels (in SD units/year) for each income level as well as the difference in happiness between them (∆).
Figure S2 legend: The difference (∆) in happiness between a household income of $40K per year and a household income of $75K per year has increased between 2002 and 2018.
Figure S2 shows the disparity in happiness between two fixed income levels, $40K/year (below the change points) and $75K/year (above the change points). In 2002, a household income of $40K/year achieved a near average level of happiness relative to everyone else that year, however by 2018 happiness had declined to lower than average levels relative to the population. By contrast, a household income of $75K/year enjoyed a higher than average level of happiness for the entire period. The difference (∆) in happiness between these two income levels doubled over the period. The increasing disparity in happiness between the rich and the poor implies that happiness has became more inequitable over the period.
Figure S3 legend: The joint distribution between residual and fitted values shows no common patterns across years and appears clustered around zero in each case.
Examination of the residual plots from the piecewise models of happiness confirms the residuals were evenly distributed around zero and there was little indication of heterscedascity. Overall, there was little evidence that the piecewise models of happiness were not appropriate for the data.
There were df = 59,876 total observations. 4000 samples (post-warmup) were drawn using sampling(NUTS). For each parameter, Bulk_ESS and Tail_ESS are effective sample size (ESS) measures, and Rhat is the potential scale reduction factor on split chains. In each case the Rhat apprached 1, indicating convergance. The smallest ESS was n = 472, which is greater than a conservative estimate of the sufficient n for estimation (n > 300).
The Bayes R2 = 0.04 ±0.001 (95%CI 0.037 — 0.043)
Coefficient definitions:
alpha is the log value of wealth (x) at the changepoint
b0 is the intercept denoting the expected value of wellbeing (y) at the changepoint
b1 is the linear slope before the changepoint
b2 is the linear slope after the changepoint
b3 is the coefficient of education (graduate)
b4 is the coefficient of age
b5 is the coefficient of age2
b6 is the coefficient of sex (male)
Parameter | Year | Estimate | Est.Error | l-95% CI | u-95% CI | Rhat | Bulk_ESS | Tail_ESS |
alpha | 2018 | -2.552 | 0.075 | -2.718 | -2.415 | 1.0 | 5472 | 4824 |
2017 | -2.656 | 0.079 | -2.816 | -2.522 | 1.0 | 4303 | 7063 | |
2016 | -2.731 | 0.074 | -2.860 | -2.584 | 1.0 | 6384 | 8892 | |
2015 | -2.665 | 0.130 | -2.921 | -2.448 | 1.0 | 2834 | 6203 | |
2014 | -2.866 | 0.115 | -3.041 | -2.570 | 1.0 | 4085 | 2740 | |
2013 | -2.702 | 0.083 | -2.866 | -2.545 | 1.0 | 6171 | 7550 | |
2012 | -2.753 | 0.066 | -2.873 | -2.609 | 1.0 | 6740 | 6462 | |
2011 | -2.943 | 0.065 | -3.072 | -2.824 | 1.0 | 7073 | 7835 | |
2010 | -3.008 | 0.133 | -3.247 | -2.697 | 1.0 | 4151 | 3470 | |
2009 | -2.674 | 0.127 | -2.938 | -2.450 | 1.0 | 3873 | 4590 | |
2008 | -2.782 | 0.266 | -3.041 | -2.238 | 1.0 | 219 | 1146 | |
2007 | -2.997 | 0.059 | -3.110 | -2.876 | 1.0 | 5871 | 6139 | |
2006 | -2.956 | 0.094 | -3.118 | -2.753 | 1.0 | 5444 | 6112 | |
2005 | -2.840 | 0.093 | -3.000 | -2.641 | 1.0 | 4800 | 5441 | |
2004 | -2.877 | 0.131 | -3.110 | -2.562 | 1.0 | 4662 | 4143 | |
2003 | -2.487 | 0.146 | -2.890 | -2.250 | 1.0 | 4154 | 2080 | |
2002 | -3.057 | 0.107 | -3.226 | -2.785 | 1.0 | 5454 | 3289 | |
b0 | 2018 | 0.053 | 0.030 | -0.008 | 0.112 | 1.0 | 5543 | 6064 |
2017 | 0.027 | 0.029 | -0.030 | 0.081 | 1.0 | 4590 | 8059 | |
2016 | -0.006 | 0.026 | -0.056 | 0.046 | 1.0 | 6825 | 8114 | |
2015 | 0.023 | 0.042 | -0.058 | 0.099 | 1.0 | 2840 | 6338 | |
2014 | -0.032 | 0.033 | -0.086 | 0.045 | 1.0 | 4131 | 3059 | |
2013 | -0.021 | 0.028 | -0.075 | 0.033 | 1.0 | 6824 | 7844 | |
2012 | -0.014 | 0.026 | -0.063 | 0.040 | 1.0 | 7029 | 7528 | |
2011 | -0.045 | 0.025 | -0.093 | 0.004 | 1.0 | 7107 | 7751 | |
2010 | -0.068 | 0.034 | -0.130 | 0.006 | 1.0 | 4298 | 4104 | |
2009 | 0.011 | 0.043 | -0.071 | 0.096 | 1.0 | 4157 | 6108 | |
2008 | 0.026 | 0.084 | -0.068 | 0.212 | 1.0 | 236 | 1276 | |
2007 | 0.004 | 0.024 | -0.042 | 0.051 | 1.0 | 6508 | 7207 | |
2006 | 0.001 | 0.033 | -0.059 | 0.069 | 1.0 | 5604 | 6302 | |
2005 | 0.036 | 0.035 | -0.026 | 0.112 | 1.0 | 5091 | 5838 | |
2004 | 0.019 | 0.047 | -0.059 | 0.130 | 1.0 | 4828 | 4394 | |
2003 | 0.171 | 0.061 | 0.025 | 0.282 | 1.0 | 4225 | 2312 | |
2002 | -0.003 | 0.030 | -0.057 | 0.063 | 1.0 | 5438 | 4220 | |
b1 | 2018 | 0.087 | 0.008 | 0.074 | 0.104 | 1.0 | 7858 | 5682 |
2017 | 0.099 | 0.010 | 0.082 | 0.120 | 1.0 | 5024 | 7076 | |
2016 | 0.100 | 0.010 | 0.082 | 0.119 | 1.0 | 7907 | 8694 | |
2015 | 0.095 | 0.014 | 0.074 | 0.126 | 1.0 | 3187 | 6110 | |
2014 | 0.110 | 0.016 | 0.079 | 0.141 | 1.0 | 4580 | 3570 | |
2013 | 0.091 | 0.010 | 0.073 | 0.111 | 1.0 | 7719 | 8334 | |
2012 | 0.104 | 0.010 | 0.085 | 0.123 | 1.0 | 8166 | 7897 | |
2011 | 0.136 | 0.013 | 0.111 | 0.163 | 1.0 | 8426 | 8048 | |
2010 | 0.125 | 0.022 | 0.083 | 0.175 | 1.0 | 4707 | 4598 | |
2009 | 0.095 | 0.013 | 0.074 | 0.124 | 1.0 | 4542 | 5573 | |
2008 | 0.112 | 0.025 | 0.067 | 0.150 | 1.0 | 232 | 992 | |
2007 | 0.145 | 0.015 | 0.117 | 0.175 | 1.0 | 7079 | 7785 | |
2006 | 0.127 | 0.016 | 0.098 | 0.159 | 1.0 | 7184 | 7679 | |
2005 | 0.115 | 0.013 | 0.091 | 0.141 | 1.0 | 6325 | 7057 | |
2004 | 0.112 | 0.015 | 0.084 | 0.141 | 1.0 | 5623 | 6230 | |
2003 | 0.079 | 0.009 | 0.066 | 0.100 | 1.0 | 5136 | 2616 | |
2002 | 0.112 | 0.016 | 0.079 | 0.143 | 1.0 | 6085 | 4885 | |
b2 | 2018 | 0.010 | 0.003 | 0.004 | 0.017 | 1.0 | 10196 | 8753 |
2017 | 0.008 | 0.003 | 0.003 | 0.013 | 1.0 | 9390 | 9529 | |
2016 | 0.011 | 0.003 | 0.005 | 0.016 | 1.0 | 12250 | 10342 | |
2015 | 0.012 | 0.004 | 0.004 | 0.020 | 1.0 | 4064 | 7318 | |
2014 | 0.016 | 0.003 | 0.009 | 0.022 | 1.0 | 6872 | 5256 | |
2013 | 0.010 | 0.003 | 0.004 | 0.016 | 1.0 | 11528 | 9635 | |
2012 | 0.014 | 0.003 | 0.007 | 0.020 | 1.0 | 11725 | 9370 | |
2011 | 0.016 | 0.003 | 0.010 | 0.022 | 1.0 | 11718 | 9541 | |
2010 | 0.016 | 0.003 | 0.009 | 0.022 | 1.0 | 7483 | 7315 | |
2009 | 0.012 | 0.004 | 0.003 | 0.020 | 1.0 | 6532 | 8426 | |
2008 | 0.013 | 0.006 | -0.001 | 0.021 | 1.0 | 215 | 1065 | |
2007 | 0.009 | 0.003 | 0.003 | 0.014 | 1.0 | 13676 | 9974 | |
2006 | 0.020 | 0.004 | 0.012 | 0.028 | 1.0 | 9227 | 8810 | |
2005 | 0.014 | 0.005 | 0.004 | 0.023 | 1.0 | 8652 | 7631 | |
2004 | 0.022 | 0.006 | 0.011 | 0.033 | 1.0 | 6852 | 6478 | |
2003 | 0.011 | 0.007 | -0.003 | 0.027 | 1.0 | 5406 | 3546 | |
2002 | 0.013 | 0.005 | 0.004 | 0.022 | 1.0 | 9130 | 6416 | |
b3 | 2018 | 0.074 | 0.019 | 0.037 | 0.111 | 1.0 | 11204 | 8453 |
2017 | 0.072 | 0.019 | 0.035 | 0.109 | 1.0 | 11049 | 9233 | |
2016 | 0.074 | 0.019 | 0.037 | 0.111 | 1.0 | 12188 | 9126 | |
2015 | 0.064 | 0.020 | 0.025 | 0.103 | 1.0 | 9486 | 8202 | |
2014 | 0.049 | 0.020 | 0.010 | 0.089 | 1.0 | 11251 | 8389 | |
2013 | 0.076 | 0.020 | 0.037 | 0.115 | 1.0 | 12362 | 8848 | |
2012 | 0.061 | 0.021 | 0.021 | 0.101 | 1.0 | 10996 | 8265 | |
2011 | 0.064 | 0.021 | 0.024 | 0.105 | 1.0 | 12069 | 8070 | |
2010 | 0.052 | 0.024 | 0.006 | 0.098 | 1.0 | 10971 | 8286 | |
2009 | 0.041 | 0.024 | -0.007 | 0.088 | 1.0 | 10339 | 8838 | |
2008 | 0.025 | 0.027 | -0.027 | 0.077 | 1.0 | 1392 | 3913 | |
2007 | 0.038 | 0.025 | -0.012 | 0.085 | 1.0 | 11273 | 8480 | |
2006 | 0.051 | 0.024 | 0.004 | 0.098 | 1.0 | 12284 | 8855 | |
2005 | 0.068 | 0.025 | 0.019 | 0.116 | 1.0 | 11291 | 9193 | |
2004 | 0.042 | 0.025 | -0.005 | 0.092 | 1.0 | 10005 | 9062 | |
2003 | 0.001 | 0.025 | -0.048 | 0.049 | 1.0 | 10346 | 7768 | |
2002 | 0.056 | 0.025 | 0.008 | 0.105 | 1.0 | 7902 | 6784 | |
b4 | 2018 | 0.162 | 0.016 | 0.130 | 0.194 | 1.0 | 12231 | 8891 |
2017 | 0.159 | 0.016 | 0.128 | 0.191 | 1.0 | 12208 | 8685 | |
2016 | 0.165 | 0.016 | 0.132 | 0.197 | 1.0 | 12478 | 7904 | |
2015 | 0.160 | 0.017 | 0.127 | 0.192 | 1.0 | 10573 | 8426 | |
2014 | 0.130 | 0.017 | 0.098 | 0.163 | 1.0 | 10748 | 8904 | |
2013 | 0.160 | 0.017 | 0.126 | 0.194 | 1.0 | 12993 | 7821 | |
2012 | 0.167 | 0.017 | 0.134 | 0.200 | 1.0 | 11112 | 8556 | |
2011 | 0.136 | 0.017 | 0.103 | 0.167 | 1.0 | 12033 | 8945 | |
2010 | 0.180 | 0.019 | 0.143 | 0.217 | 1.0 | 9835 | 8565 | |
2009 | 0.173 | 0.019 | 0.135 | 0.211 | 1.0 | 10287 | 9023 | |
2008 | 0.146 | 0.020 | 0.107 | 0.186 | 1.0 | 8738 | 8148 | |
2007 | 0.152 | 0.019 | 0.113 | 0.190 | 1.0 | 10375 | 8168 | |
2006 | 0.137 | 0.019 | 0.099 | 0.175 | 1.0 | 12977 | 8755 | |
2005 | 0.138 | 0.019 | 0.100 | 0.176 | 1.0 | 11787 | 8765 | |
2004 | 0.161 | 0.019 | 0.123 | 0.199 | 1.0 | 9932 | 8377 | |
2003 | 0.139 | 0.020 | 0.100 | 0.178 | 1.0 | 11440 | 8457 | |
2002 | 0.146 | 0.019 | 0.109 | 0.183 | 1.0 | 7931 | 7351 | |
b5 | 2018 | 0.132 | 0.009 | 0.115 | 0.149 | 1.0 | 13278 | 9562 |
2017 | 0.128 | 0.009 | 0.110 | 0.144 | 1.0 | 12532 | 8450 | |
2016 | 0.110 | 0.009 | 0.093 | 0.127 | 1.0 | 13529 | 8672 | |
2015 | 0.098 | 0.009 | 0.080 | 0.115 | 1.0 | 10882 | 8875 | |
2014 | 0.076 | 0.009 | 0.058 | 0.094 | 1.0 | 11956 | 8815 | |
2013 | 0.074 | 0.009 | 0.055 | 0.092 | 1.0 | 12404 | 8055 | |
2012 | 0.070 | 0.009 | 0.052 | 0.088 | 1.0 | 11601 | 8303 | |
2011 | 0.072 | 0.009 | 0.054 | 0.091 | 1.0 | 13429 | 8574 | |
2010 | 0.046 | 0.010 | 0.026 | 0.066 | 1.0 | 12143 | 8694 | |
2009 | 0.072 | 0.011 | 0.051 | 0.093 | 1.0 | 10417 | 8448 | |
2008 | 0.066 | 0.011 | 0.043 | 0.087 | 1.0 | 3095 | 6799 | |
2007 | 0.075 | 0.011 | 0.055 | 0.096 | 1.0 | 11270 | 9261 | |
2006 | 0.075 | 0.011 | 0.055 | 0.096 | 1.0 | 13602 | 8766 | |
2005 | 0.080 | 0.011 | 0.059 | 0.100 | 1.0 | 12221 | 8564 | |
2004 | 0.083 | 0.011 | 0.061 | 0.104 | 1.0 | 10224 | 8561 | |
2003 | 0.055 | 0.011 | 0.033 | 0.076 | 1.0 | 10487 | 8698 | |
2002 | 0.061 | 0.011 | 0.040 | 0.082 | 1.0 | 7262 | 7480 | |
b6 | 2018 | 0.015 | 0.008 | -0.001 | 0.031 | 1.0 | 12933 | 8532 |
2017 | 0.030 | 0.008 | 0.014 | 0.046 | 1.0 | 12266 | 8540 | |
2016 | 0.026 | 0.008 | 0.010 | 0.042 | 1.0 | 13099 | 9006 | |
2015 | 0.017 | 0.008 | 0.001 | 0.034 | 1.0 | 10727 | 8637 | |
2014 | 0.033 | 0.008 | 0.017 | 0.049 | 1.0 | 12856 | 8975 | |
2013 | 0.042 | 0.009 | 0.025 | 0.059 | 1.0 | 12639 | 8558 | |
2012 | 0.030 | 0.009 | 0.014 | 0.047 | 1.0 | 11774 | 8472 | |
2011 | 0.044 | 0.008 | 0.027 | 0.060 | 1.0 | 12339 | 8858 | |
2010 | 0.025 | 0.009 | 0.006 | 0.043 | 1.0 | 11767 | 8632 | |
2009 | 0.031 | 0.010 | 0.012 | 0.050 | 1.0 | 9995 | 8638 | |
2008 | 0.027 | 0.010 | 0.008 | 0.046 | 1.0 | 6431 | 8533 | |
2007 | 0.017 | 0.009 | -0.002 | 0.035 | 1.0 | 10701 | 8874 | |
2006 | 0.014 | 0.009 | -0.004 | 0.033 | 1.0 | 12686 | 8409 | |
2005 | 0.022 | 0.009 | 0.004 | 0.040 | 1.0 | 11749 | 8742 | |
2004 | 0.021 | 0.010 | 0.002 | 0.039 | 1.0 | 10169 | 8626 | |
2003 | 0.014 | 0.009 | -0.004 | 0.033 | 1.0 | 10804 | 9196 | |
2002 | 0.004 | 0.009 | -0.014 | 0.022 | 1.0 | 7485 | 8638 | |
b7 | 2018 | -0.013 | 0.009 | -0.032 | 0.005 | 1.0 | 14279 | 8426 |
2017 | -0.009 | 0.009 | -0.028 | 0.009 | 1.0 | 13779 | 8245 | |
2016 | -0.001 | 0.009 | -0.018 | 0.016 | 1.0 | 14702 | 8782 | |
2015 | -0.002 | 0.009 | -0.020 | 0.017 | 1.0 | 11501 | 8795 | |
2014 | 0.002 | 0.010 | -0.018 | 0.022 | 1.0 | 12714 | 8434 | |
2013 | 0.016 | 0.010 | -0.003 | 0.035 | 1.0 | 14291 | 9040 | |
2012 | 0.019 | 0.010 | -0.001 | 0.039 | 1.0 | 11738 | 8830 | |
2011 | 0.011 | 0.009 | -0.007 | 0.030 | 1.0 | 13366 | 8342 | |
2010 | -0.017 | 0.011 | -0.039 | 0.004 | 1.0 | 12658 | 8195 | |
2009 | -0.030 | 0.012 | -0.052 | -0.007 | 1.0 | 12408 | 8936 | |
2008 | -0.023 | 0.012 | -0.047 | 0.001 | 1.0 | 9680 | 8078 | |
2007 | -0.024 | 0.011 | -0.046 | -0.001 | 1.0 | 12640 | 8804 | |
2006 | -0.031 | 0.012 | -0.054 | -0.008 | 1.0 | 14266 | 8299 | |
2005 | -0.045 | 0.012 | -0.070 | -0.021 | 1.0 | 12913 | 8511 | |
2004 | -0.032 | 0.013 | -0.057 | -0.008 | 1.0 | 11245 | 8975 | |
2003 | -0.028 | 0.013 | -0.053 | -0.004 | 1.0 | 11529 | 8548 | |
2002 | -0.058 | 0.012 | -0.082 | -0.034 | 1.0 | 9952 | 8211 | |
sigma | 2018 | 0.974 | 0.006 | 0.963 | 0.986 | 1.0 | 15655 | 7673 |
2017 | 0.976 | 0.006 | 0.964 | 0.987 | 1.0 | 15506 | 8441 | |
2016 | 0.979 | 0.006 | 0.968 | 0.990 | 1.0 | 16132 | 9200 | |
2015 | 0.979 | 0.006 | 0.968 | 0.991 | 1.0 | 13711 | 8663 | |
2014 | 0.983 | 0.006 | 0.971 | 0.994 | 1.0 | 16124 | 8688 | |
2013 | 0.982 | 0.006 | 0.970 | 0.994 | 1.0 | 15219 | 8271 | |
2012 | 0.979 | 0.006 | 0.968 | 0.991 | 1.0 | 13360 | 9337 | |
2011 | 0.980 | 0.006 | 0.969 | 0.992 | 1.0 | 14503 | 9353 | |
2010 | 0.983 | 0.007 | 0.970 | 0.997 | 1.0 | 15065 | 8299 | |
2009 | 0.981 | 0.007 | 0.967 | 0.994 | 1.0 | 13659 | 8781 | |
2008 | 0.982 | 0.007 | 0.969 | 0.996 | 1.0 | 10357 | 8886 | |
2007 | 0.982 | 0.007 | 0.969 | 0.995 | 1.0 | 14836 | 9236 | |
2006 | 0.981 | 0.007 | 0.968 | 0.994 | 1.0 | 15746 | 8408 | |
2005 | 0.980 | 0.007 | 0.967 | 0.993 | 1.0 | 14754 | 8100 | |
2004 | 0.980 | 0.007 | 0.967 | 0.994 | 1.0 | 12247 | 8967 | |
2003 | 0.984 | 0.007 | 0.971 | 0.998 | 1.0 | 12670 | 8064 | |
2002 | 0.987 | 0.007 | 0.973 | 1.000 | 1.0 | 7527 | 6712 |
Parameter | Year | Estimate | Est.Error | l-95% CI | u-95% CI | Rhat | Bulk_ESS | Tail_ESS |
Intercept | 2018 | -0.316 | 0.019 | -0.353 | -0.277 | 1.0 | 14006 | 10228 |
2017 | -0.291 | 0.019 | -0.329 | -0.253 | 1.0 | 13073 | 10321 | |
2016 | -0.306 | 0.019 | -0.344 | -0.268 | 1.0 | 14068 | 10370 | |
2015 | -0.313 | 0.020 | -0.353 | -0.274 | 1.0 | 13763 | 10488 | |
2014 | -0.297 | 0.020 | -0.335 | -0.258 | 1.0 | 14018 | 10053 | |
2013 | -0.312 | 0.020 | -0.351 | -0.272 | 1.0 | 15651 | 10085 | |
2012 | -0.334 | 0.020 | -0.374 | -0.294 | 1.0 | 15044 | 9419 | |
2011 | -0.329 | 0.020 | -0.368 | -0.288 | 1.0 | 15264 | 10032 | |
2010 | -0.293 | 0.023 | -0.338 | -0.250 | 1.0 | 15413 | 10151 | |
2009 | -0.322 | 0.023 | -0.368 | -0.276 | 1.0 | 15612 | 10143 | |
2008 | -0.286 | 0.023 | -0.332 | -0.242 | 1.0 | 14927 | 10486 | |
2007 | -0.234 | 0.022 | -0.278 | -0.192 | 1.0 | 14104 | 10340 | |
2006 | -0.300 | 0.023 | -0.344 | -0.255 | 1.0 | 14512 | 9458 | |
2005 | -0.304 | 0.023 | -0.350 | -0.258 | 1.0 | 18269 | 9269 | |
2004 | -0.337 | 0.023 | -0.383 | -0.291 | 1.0 | 16123 | 9961 | |
2003 | -0.300 | 0.023 | -0.345 | -0.255 | 1.0 | 14964 | 10083 | |
2002 | -0.237 | 0.022 | -0.280 | -0.193 | 1.0 | 15569 | 9592 | |
dollars | 2018 | 0.033 | 0.002 | 0.029 | 0.037 | 1.0 | 19127 | 9998 |
2017 | 0.027 | 0.002 | 0.024 | 0.031 | 1.0 | 18387 | 10060 | |
2016 | 0.030 | 0.002 | 0.026 | 0.034 | 1.0 | 19864 | 10204 | |
2015 | 0.034 | 0.002 | 0.029 | 0.038 | 1.0 | 20147 | 10087 | |
2014 | 0.031 | 0.002 | 0.027 | 0.035 | 1.0 | 20813 | 9558 | |
2013 | 0.029 | 0.002 | 0.025 | 0.033 | 1.0 | 20564 | 9776 | |
2012 | 0.035 | 0.002 | 0.031 | 0.040 | 1.0 | 19263 | 9816 | |
2011 | 0.035 | 0.002 | 0.030 | 0.039 | 1.0 | 18440 | 9290 | |
2010 | 0.030 | 0.002 | 0.025 | 0.034 | 1.0 | 19683 | 10210 | |
2009 | 0.034 | 0.003 | 0.029 | 0.039 | 1.0 | 19411 | 10133 | |
2008 | 0.032 | 0.002 | 0.027 | 0.037 | 1.0 | 19275 | 10239 | |
2007 | 0.025 | 0.002 | 0.021 | 0.030 | 1.0 | 20606 | 9870 | |
2006 | 0.040 | 0.003 | 0.034 | 0.045 | 1.0 | 20396 | 10117 | |
2005 | 0.040 | 0.003 | 0.034 | 0.046 | 1.0 | 22024 | 9664 | |
2004 | 0.048 | 0.003 | 0.041 | 0.054 | 1.0 | 19019 | 9389 | |
2003 | 0.046 | 0.003 | 0.039 | 0.052 | 1.0 | 17897 | 9692 | |
2002 | 0.033 | 0.003 | 0.027 | 0.039 | 1.0 | 19647 | 9792 | |
grad | 2018 | 0.103 | 0.019 | 0.066 | 0.140 | 1.0 | 11657 | 8807 |
2017 | 0.108 | 0.019 | 0.071 | 0.145 | 1.0 | 10077 | 8584 | |
2016 | 0.098 | 0.019 | 0.061 | 0.136 | 1.0 | 9644 | 8660 | |
2015 | 0.086 | 0.020 | 0.048 | 0.124 | 1.0 | 11031 | 8890 | |
2014 | 0.068 | 0.020 | 0.029 | 0.105 | 1.0 | 11203 | 8900 | |
2013 | 0.097 | 0.020 | 0.058 | 0.136 | 1.0 | 12095 | 8973 | |
2012 | 0.078 | 0.020 | 0.039 | 0.118 | 1.0 | 10996 | 9294 | |
2011 | 0.079 | 0.020 | 0.039 | 0.119 | 1.0 | 12104 | 8737 | |
2010 | 0.064 | 0.023 | 0.018 | 0.110 | 1.0 | 12782 | 8831 | |
2009 | 0.064 | 0.024 | 0.017 | 0.111 | 1.0 | 12111 | 8978 | |
2008 | 0.054 | 0.025 | 0.006 | 0.103 | 1.0 | 12808 | 8695 | |
2007 | 0.067 | 0.024 | 0.020 | 0.114 | 1.0 | 10230 | 8570 | |
2006 | 0.071 | 0.024 | 0.024 | 0.118 | 1.0 | 11556 | 9107 | |
2005 | 0.096 | 0.025 | 0.047 | 0.145 | 1.0 | 15613 | 9054 | |
2004 | 0.060 | 0.025 | 0.011 | 0.108 | 1.0 | 10952 | 9517 | |
2003 | 0.027 | 0.025 | -0.022 | 0.076 | 1.0 | 11297 | 9208 | |
2002 | 0.069 | 0.025 | 0.021 | 0.118 | 1.0 | 12773 | 8684 | |
age | 2018 | 0.115 | 0.009 | 0.098 | 0.132 | 1.0 | 11227 | 9635 |
2017 | 0.106 | 0.009 | 0.090 | 0.123 | 1.0 | 11325 | 8997 | |
2016 | 0.091 | 0.009 | 0.075 | 0.108 | 1.0 | 12091 | 8374 | |
2015 | 0.082 | 0.009 | 0.064 | 0.099 | 1.0 | 10567 | 8693 | |
2014 | 0.058 | 0.009 | 0.040 | 0.076 | 1.0 | 10989 | 8467 | |
2013 | 0.056 | 0.009 | 0.038 | 0.074 | 1.0 | 12008 | 9546 | |
2012 | 0.049 | 0.009 | 0.032 | 0.067 | 1.0 | 11331 | 9625 | |
2011 | 0.050 | 0.009 | 0.032 | 0.068 | 1.0 | 13077 | 9763 | |
2010 | 0.027 | 0.010 | 0.006 | 0.047 | 1.0 | 10760 | 8808 | |
2009 | 0.047 | 0.011 | 0.026 | 0.068 | 1.0 | 10922 | 8987 | |
2008 | 0.041 | 0.011 | 0.021 | 0.062 | 1.0 | 12210 | 9086 | |
2007 | 0.048 | 0.011 | 0.028 | 0.068 | 1.0 | 12197 | 10017 | |
2006 | 0.054 | 0.010 | 0.033 | 0.074 | 1.0 | 11566 | 9238 | |
2005 | 0.059 | 0.011 | 0.038 | 0.080 | 1.0 | 14325 | 9516 | |
2004 | 0.066 | 0.011 | 0.045 | 0.087 | 1.0 | 11391 | 9310 | |
2003 | 0.043 | 0.011 | 0.022 | 0.064 | 1.0 | 12258 | 9349 | |
2002 | 0.045 | 0.011 | 0.024 | 0.066 | 1.0 | 11233 | 8473 | |
age_sq | 2018 | -0.001 | 0.008 | -0.017 | 0.015 | 1.0 | 11109 | 8882 |
2017 | 0.010 | 0.008 | -0.006 | 0.026 | 1.0 | 10722 | 8526 | |
2016 | 0.010 | 0.008 | -0.006 | 0.026 | 1.0 | 10926 | 8888 | |
2015 | 0.002 | 0.008 | -0.014 | 0.018 | 1.0 | 10702 | 8938 | |
2014 | 0.018 | 0.008 | 0.002 | 0.034 | 1.0 | 10944 | 8950 | |
2013 | 0.026 | 0.008 | 0.009 | 0.042 | 1.0 | 11501 | 9677 | |
2012 | 0.014 | 0.008 | -0.003 | 0.030 | 1.0 | 11191 | 8770 | |
2011 | 0.025 | 0.008 | 0.009 | 0.041 | 1.0 | 12111 | 9170 | |
2010 | 0.011 | 0.009 | -0.007 | 0.029 | 1.0 | 11752 | 9509 | |
2009 | 0.016 | 0.009 | -0.003 | 0.034 | 1.0 | 11600 | 9348 | |
2008 | 0.012 | 0.010 | -0.008 | 0.030 | 1.0 | 11560 | 9064 | |
2007 | -0.002 | 0.010 | -0.021 | 0.017 | 1.0 | 10630 | 8049 | |
2006 | -0.000 | 0.009 | -0.018 | 0.018 | 1.0 | 11386 | 8843 | |
2005 | 0.008 | 0.009 | -0.010 | 0.026 | 1.0 | 14429 | 8527 | |
2004 | 0.009 | 0.009 | -0.009 | 0.028 | 1.0 | 11468 | 9210 | |
2003 | 0.007 | 0.009 | -0.011 | 0.025 | 1.0 | 11813 | 8675 | |
2002 | -0.009 | 0.009 | -0.026 | 0.010 | 1.0 | 11330 | 9643 | |
male | 2018 | 0.171 | 0.016 | 0.138 | 0.203 | 1.0 | 12081 | 8698 |
2017 | 0.170 | 0.016 | 0.138 | 0.202 | 1.0 | 11135 | 7889 | |
2016 | 0.174 | 0.016 | 0.142 | 0.207 | 1.0 | 11233 | 8879 | |
2015 | 0.167 | 0.017 | 0.134 | 0.200 | 1.0 | 11220 | 8949 | |
2014 | 0.138 | 0.017 | 0.104 | 0.170 | 1.0 | 10685 | 9161 | |
2013 | 0.169 | 0.017 | 0.136 | 0.202 | 1.0 | 11261 | 8336 | |
2012 | 0.177 | 0.017 | 0.143 | 0.209 | 1.0 | 9968 | 8683 | |
2011 | 0.148 | 0.017 | 0.115 | 0.181 | 1.0 | 10976 | 8591 | |
2010 | 0.188 | 0.019 | 0.151 | 0.225 | 1.0 | 13088 | 9238 | |
2009 | 0.183 | 0.020 | 0.145 | 0.221 | 1.0 | 11448 | 8924 | |
2008 | 0.155 | 0.020 | 0.116 | 0.194 | 1.0 | 12673 | 9016 | |
2007 | 0.164 | 0.020 | 0.125 | 0.202 | 1.0 | 10811 | 8779 | |
2006 | 0.146 | 0.019 | 0.108 | 0.184 | 1.0 | 12257 | 8727 | |
2005 | 0.145 | 0.019 | 0.108 | 0.183 | 1.0 | 16872 | 9600 | |
2004 | 0.168 | 0.019 | 0.130 | 0.206 | 1.0 | 12085 | 9283 | |
2003 | 0.144 | 0.019 | 0.107 | 0.182 | 1.0 | 13152 | 9230 | |
2002 | 0.153 | 0.019 | 0.116 | 0.191 | 1.0 | 13412 | 9750 | |
sigma | 2018 | 0.979 | 0.006 | 0.968 | 0.991 | 1.0 | 14442 | 9369 |
2017 | 0.982 | 0.006 | 0.971 | 0.993 | 1.0 | 13014 | 8298 | |
2016 | 0.983 | 0.006 | 0.972 | 0.995 | 1.0 | 14319 | 8855 | |
2015 | 0.984 | 0.006 | 0.972 | 0.995 | 1.0 | 15810 | 8843 | |
2014 | 0.987 | 0.006 | 0.975 | 0.999 | 1.0 | 12493 | 8776 | |
2013 | 0.986 | 0.006 | 0.974 | 0.998 | 1.0 | 12853 | 9242 | |
2012 | 0.984 | 0.006 | 0.972 | 0.996 | 1.0 | 14535 | 9003 | |
2011 | 0.985 | 0.006 | 0.974 | 0.997 | 1.0 | 14082 | 9203 | |
2010 | 0.987 | 0.007 | 0.974 | 1.001 | 1.0 | 15396 | 8926 | |
2009 | 0.985 | 0.007 | 0.972 | 0.999 | 1.0 | 15378 | 9419 | |
2008 | 0.987 | 0.007 | 0.973 | 1.001 | 1.0 | 14429 | 8890 | |
2007 | 0.989 | 0.007 | 0.976 | 1.003 | 1.0 | 13405 | 9885 | |
2006 | 0.985 | 0.007 | 0.972 | 0.998 | 1.0 | 13470 | 9216 | |
2005 | 0.986 | 0.007 | 0.972 | 1.000 | 1.0 | 18106 | 9150 | |
2004 | 0.983 | 0.007 | 0.970 | 0.997 | 1.0 | 13797 | 8844 | |
2003 | 0.987 | 0.007 | 0.974 | 1.000 | 1.0 | 15662 | 8452 | |
2002 | 0.990 | 0.007 | 0.977 | 1.004 | 1.0 | 15600 | 9265 |
Parameter | Year | Estimate | Est.Error | l-95% CI | u-95% CI | Rhat | Bulk_ESS | Tail_ESS |
alpha | 2018 | -3.009 | 0.087 | -3.159 | -2.825 | 1.0 | 5796 | 6401 |
2017 | -2.591 | 0.128 | -2.835 | -2.371 | 1.0 | 3522 | 7302 | |
2016 | -2.848 | 0.120 | -3.052 | -2.557 | 1.0 | 2882 | 2724 | |
2015 | -2.543 | 0.148 | -3.034 | -2.355 | 1.0 | 2345 | 752 | |
2014 | -2.419 | 0.073 | -2.587 | -2.287 | 1.0 | 6196 | 3543 | |
2013 | -2.809 | 0.077 | -2.946 | -2.647 | 1.0 | 5706 | 6100 | |
2012 | -2.744 | 0.060 | -2.854 | -2.617 | 1.0 | 6608 | 5786 | |
2011 | -3.052 | 0.110 | -3.245 | -2.839 | 1.0 | 3674 | 8091 | |
2010 | -2.097 | 0.165 | -2.471 | -1.816 | 1.0 | 5211 | 4410 | |
2009 | -2.933 | 0.206 | -3.259 | -2.539 | 1.0 | 2544 | 6140 | |
2008 | -2.291 | 0.217 | -2.743 | -1.826 | 1.0 | 3370 | 2947 | |
2007 | -2.762 | 0.172 | -3.062 | -2.325 | 1.0 | 3736 | 2942 | |
2006 | 0.150 | 2.619 | -3.305 | 5.689 | 1.5 | 7 | 122 | |
2005 | -2.225 | 0.324 | -2.795 | -1.513 | 1.0 | 2470 | 2825 | |
2004 | -3.107 | 0.378 | -3.564 | -2.223 | 1.0 | 1913 | 3248 | |
2003 | -2.646 | 0.190 | -2.983 | -2.256 | 1.0 | 4233 | 5396 | |
2002 | -3.038 | 0.295 | -3.530 | -2.380 | 1.0 | 3088 | 3259 | |
b0 | 2018 | -0.068 | 0.025 | -0.114 | -0.018 | 1.0 | 6309 | 7242 |
2017 | 0.056 | 0.038 | -0.015 | 0.128 | 1.0 | 3505 | 6850 | |
2016 | -0.036 | 0.032 | -0.092 | 0.038 | 1.0 | 2962 | 2360 | |
2015 | 0.031 | 0.042 | -0.087 | 0.096 | 1.0 | 2239 | 795 | |
2014 | 0.094 | 0.028 | 0.035 | 0.148 | 1.0 | 5861 | 4248 | |
2013 | -0.014 | 0.024 | -0.059 | 0.035 | 1.0 | 6436 | 6114 | |
2012 | -0.016 | 0.022 | -0.059 | 0.030 | 1.0 | 6943 | 6921 | |
2011 | -0.058 | 0.028 | -0.109 | -0.002 | 1.0 | 3975 | 6762 | |
2010 | 0.129 | 0.056 | 0.015 | 0.237 | 1.0 | 5496 | 5272 | |
2009 | -0.031 | 0.043 | -0.101 | 0.059 | 1.0 | 2400 | 6255 | |
2008 | 0.122 | 0.068 | 0.001 | 0.271 | 1.0 | 3384 | 2988 | |
2007 | 0.074 | 0.041 | 0.007 | 0.177 | 1.0 | 3712 | 3056 | |
2006 | 1.126 | 0.944 | -0.073 | 2.599 | 1.5 | 7 | 91 | |
2005 | 0.217 | 0.125 | 0.040 | 0.521 | 1.0 | 2533 | 2776 | |
2004 | 0.033 | 0.084 | -0.065 | 0.249 | 1.0 | 1917 | 3027 | |
2003 | 0.134 | 0.057 | 0.039 | 0.258 | 1.0 | 4440 | 5418 | |
2002 | 0.027 | 0.060 | -0.067 | 0.170 | 1.0 | 3120 | 3468 | |
b1 | 2018 | 0.115 | 0.015 | 0.087 | 0.145 | 1.0 | 6905 | 8168 |
2017 | 0.077 | 0.010 | 0.061 | 0.100 | 1.0 | 4224 | 6443 | |
2016 | 0.098 | 0.014 | 0.070 | 0.128 | 1.0 | 3495 | 3178 | |
2015 | 0.070 | 0.012 | 0.056 | 0.106 | 1.0 | 2591 | 811 | |
2014 | 0.064 | 0.005 | 0.055 | 0.075 | 1.0 | 8802 | 6392 | |
2013 | 0.088 | 0.009 | 0.070 | 0.107 | 1.0 | 7204 | 7706 | |
2012 | 0.087 | 0.008 | 0.072 | 0.102 | 1.0 | 8564 | 7777 | |
2011 | 0.124 | 0.018 | 0.092 | 0.162 | 1.0 | 4164 | 7290 | |
2010 | 0.043 | 0.005 | 0.034 | 0.054 | 1.0 | 7594 | 6355 | |
2009 | 0.089 | 0.020 | 0.058 | 0.128 | 1.0 | 2771 | 7262 | |
2008 | 0.050 | 0.007 | 0.038 | 0.067 | 1.0 | 4919 | 4199 | |
2007 | 0.077 | 0.014 | 0.051 | 0.105 | 1.0 | 4578 | 4413 | |
2006 | 0.033 | 0.023 | 0.021 | 0.074 | 1.3 | 9 | 101 | |
2005 | 0.050 | 0.007 | 0.038 | 0.065 | 1.0 | 4076 | 4885 | |
2004 | 0.099 | 0.034 | 0.049 | 0.167 | 1.0 | 2046 | 4384 | |
2003 | 0.067 | 0.010 | 0.050 | 0.088 | 1.0 | 5513 | 6127 | |
2002 | 0.086 | 0.026 | 0.049 | 0.149 | 1.0 | 3470 | 5376 | |
b2 | 2018 | 0.018 | 0.003 | 0.013 | 0.023 | 1.0 | 11457 | 9423 |
2017 | 0.009 | 0.003 | 0.003 | 0.015 | 1.0 | 6091 | 7618 | |
2016 | 0.014 | 0.003 | 0.007 | 0.019 | 1.0 | 5105 | 4907 | |
2015 | 0.012 | 0.004 | 0.005 | 0.021 | 1.0 | 2956 | 1315 | |
2014 | 0.010 | 0.003 | 0.004 | 0.016 | 1.0 | 9955 | 7475 | |
2013 | 0.015 | 0.003 | 0.009 | 0.020 | 1.0 | 10976 | 8677 | |
2012 | 0.012 | 0.003 | 0.006 | 0.018 | 1.0 | 13160 | 9581 | |
2011 | 0.017 | 0.003 | 0.011 | 0.022 | 1.0 | 7133 | 8981 | |
2010 | 0.002 | 0.005 | -0.008 | 0.012 | 1.0 | 7857 | 7330 | |
2009 | 0.014 | 0.004 | 0.006 | 0.021 | 1.0 | 4111 | 7159 | |
2008 | 0.007 | 0.005 | -0.003 | 0.016 | 1.0 | 5080 | 4397 | |
2007 | 0.008 | 0.003 | 0.001 | 0.014 | 1.0 | 5986 | 6240 | |
2006 | 0.005 | 2.257 | -5.187 | 5.088 | 1.4 | 1698 | 406 | |
2005 | 0.009 | 0.009 | -0.009 | 0.023 | 1.0 | 3654 | 3400 | |
2004 | 0.022 | 0.007 | 0.005 | 0.032 | 1.0 | 2627 | 3807 | |
2003 | 0.012 | 0.007 | -0.003 | 0.024 | 1.0 | 6270 | 6729 | |
2002 | 0.018 | 0.006 | 0.005 | 0.028 | 1.0 | 4458 | 4674 | |
b3 | 2018 | 0.009 | 0.018 | -0.027 | 0.045 | 1.0 | 10675 | 8368 |
2017 | -0.012 | 0.019 | -0.049 | 0.025 | 1.0 | 7633 | 7876 | |
2016 | 0.008 | 0.018 | -0.028 | 0.044 | 1.0 | 8625 | 7399 | |
2015 | -0.009 | 0.019 | -0.046 | 0.029 | 1.0 | 8874 | 8246 | |
2014 | -0.017 | 0.019 | -0.054 | 0.019 | 1.0 | 10781 | 8711 | |
2013 | -0.037 | 0.019 | -0.073 | 0.000 | 1.0 | 10542 | 8903 | |
2012 | -0.009 | 0.019 | -0.047 | 0.029 | 1.0 | 9819 | 8157 | |
2011 | -0.011 | 0.019 | -0.049 | 0.026 | 1.0 | 10814 | 8505 | |
2010 | -0.021 | 0.023 | -0.065 | 0.024 | 1.0 | 9141 | 8602 | |
2009 | -0.013 | 0.023 | -0.057 | 0.032 | 1.0 | 7964 | 8206 | |
2008 | -0.043 | 0.023 | -0.089 | 0.003 | 1.0 | 10047 | 8705 | |
2007 | -0.078 | 0.024 | -0.125 | -0.031 | 1.0 | 8492 | 8387 | |
2006 | -0.036 | 0.024 | -0.083 | 0.011 | 1.0 | 145 | 5732 | |
2005 | -0.083 | 0.024 | -0.130 | -0.036 | 1.0 | 8653 | 7735 | |
2004 | -0.082 | 0.024 | -0.130 | -0.033 | 1.0 | 6691 | 7545 | |
2003 | -0.109 | 0.024 | -0.158 | -0.062 | 1.0 | 10328 | 8628 | |
2002 | -0.085 | 0.025 | -0.132 | -0.037 | 1.0 | 9829 | 7970 | |
b4 | 2018 | 0.070 | 0.008 | 0.053 | 0.086 | 1.0 | 11685 | 8285 |
2017 | 0.061 | 0.008 | 0.044 | 0.077 | 1.0 | 9594 | 8649 | |
2016 | 0.070 | 0.008 | 0.053 | 0.086 | 1.0 | 9173 | 9239 | |
2015 | 0.055 | 0.008 | 0.038 | 0.071 | 1.0 | 10474 | 8393 | |
2014 | 0.066 | 0.008 | 0.050 | 0.083 | 1.0 | 12341 | 8631 | |
2013 | 0.077 | 0.008 | 0.060 | 0.094 | 1.0 | 9937 | 8223 | |
2012 | 0.065 | 0.008 | 0.048 | 0.081 | 1.0 | 10424 | 8336 | |
2011 | 0.060 | 0.009 | 0.043 | 0.077 | 1.0 | 10762 | 8558 | |
2010 | 0.051 | 0.010 | 0.033 | 0.070 | 1.0 | 10826 | 7560 | |
2009 | 0.086 | 0.010 | 0.067 | 0.106 | 1.0 | 10700 | 8548 | |
2008 | 0.087 | 0.010 | 0.068 | 0.106 | 1.0 | 10667 | 9292 | |
2007 | 0.106 | 0.010 | 0.087 | 0.126 | 1.0 | 9486 | 7714 | |
2006 | 0.109 | 0.010 | 0.090 | 0.130 | 1.0 | 100 | 5090 | |
2005 | 0.121 | 0.010 | 0.102 | 0.141 | 1.0 | 9190 | 8563 | |
2004 | 0.128 | 0.010 | 0.108 | 0.148 | 1.0 | 9179 | 8503 | |
2003 | 0.123 | 0.010 | 0.103 | 0.143 | 1.0 | 10191 | 8337 | |
2002 | 0.129 | 0.010 | 0.109 | 0.149 | 1.0 | 10190 | 8747 | |
b5 | 2018 | 0.134 | 0.008 | 0.119 | 0.150 | 1.0 | 11021 | 8946 |
2017 | 0.118 | 0.008 | 0.103 | 0.133 | 1.0 | 8717 | 8302 | |
2016 | 0.130 | 0.008 | 0.114 | 0.145 | 1.0 | 9345 | 8519 | |
2015 | 0.131 | 0.008 | 0.116 | 0.146 | 1.0 | 11314 | 8777 | |
2014 | 0.129 | 0.008 | 0.115 | 0.144 | 1.0 | 12129 | 8086 | |
2013 | 0.130 | 0.008 | 0.115 | 0.145 | 1.0 | 11579 | 8894 | |
2012 | 0.141 | 0.008 | 0.126 | 0.156 | 1.0 | 10954 | 8394 | |
2011 | 0.135 | 0.008 | 0.120 | 0.150 | 1.0 | 9739 | 8752 | |
2010 | 0.123 | 0.009 | 0.107 | 0.140 | 1.0 | 10126 | 8895 | |
2009 | 0.111 | 0.009 | 0.094 | 0.128 | 1.0 | 9536 | 8098 | |
2008 | 0.109 | 0.009 | 0.092 | 0.126 | 1.0 | 10640 | 8690 | |
2007 | 0.081 | 0.009 | 0.064 | 0.099 | 1.0 | 9577 | 8634 | |
2006 | 0.084 | 0.009 | 0.067 | 0.101 | 1.0 | 216 | 6141 | |
2005 | 0.092 | 0.009 | 0.076 | 0.110 | 1.0 | 9211 | 8415 | |
2004 | 0.081 | 0.009 | 0.064 | 0.098 | 1.0 | 8662 | 7884 | |
2003 | 0.091 | 0.009 | 0.075 | 0.108 | 1.0 | 10073 | 8832 | |
2002 | 0.081 | 0.008 | 0.065 | 0.098 | 1.0 | 10453 | 9043 | |
b6 | 2018 | -0.063 | 0.016 | -0.094 | -0.032 | 1.0 | 10751 | 8041 |
2017 | -0.059 | 0.016 | -0.089 | -0.027 | 1.0 | 8916 | 8293 | |
2016 | -0.035 | 0.016 | -0.066 | -0.004 | 1.0 | 8853 | 8230 | |
2015 | -0.039 | 0.016 | -0.070 | -0.008 | 1.0 | 9617 | 7984 | |
2014 | -0.099 | 0.016 | -0.129 | -0.067 | 1.0 | 11675 | 8109 | |
2013 | -0.061 | 0.016 | -0.093 | -0.030 | 1.0 | 10075 | 8441 | |
2012 | -0.045 | 0.016 | -0.077 | -0.013 | 1.0 | 9777 | 8853 | |
2011 | -0.069 | 0.016 | -0.100 | -0.038 | 1.0 | 11111 | 8662 | |
2010 | -0.044 | 0.018 | -0.079 | -0.009 | 1.0 | 9624 | 7946 | |
2009 | -0.054 | 0.018 | -0.089 | -0.018 | 1.0 | 9452 | 8027 | |
2008 | -0.061 | 0.019 | -0.098 | -0.025 | 1.0 | 10248 | 7732 | |
2007 | -0.071 | 0.019 | -0.108 | -0.034 | 1.0 | 9126 | 8451 | |
2006 | -0.066 | 0.018 | -0.103 | -0.030 | 1.0 | 6185 | 6126 | |
2005 | -0.094 | 0.019 | -0.130 | -0.057 | 1.0 | 9648 | 8018 | |
2004 | -0.106 | 0.019 | -0.142 | -0.070 | 1.0 | 8243 | 7566 | |
2003 | -0.104 | 0.018 | -0.140 | -0.068 | 1.0 | 10116 | 7952 | |
2002 | -0.061 | 0.018 | -0.097 | -0.025 | 1.0 | 10694 | 7985 | |
sigma | 2018 | 0.981 | 0.005 | 0.970 | 0.991 | 1.0 | 14252 | 8298 |
2017 | 0.984 | 0.006 | 0.973 | 0.995 | 1.0 | 10967 | 8445 | |
2016 | 0.982 | 0.006 | 0.971 | 0.993 | 1.0 | 13353 | 9321 | |
2015 | 0.983 | 0.006 | 0.972 | 0.993 | 1.0 | 13255 | 8527 | |
2014 | 0.980 | 0.005 | 0.970 | 0.991 | 1.0 | 14400 | 8809 | |
2013 | 0.981 | 0.006 | 0.970 | 0.992 | 1.0 | 13524 | 8950 | |
2012 | 0.981 | 0.006 | 0.970 | 0.992 | 1.0 | 13467 | 8290 | |
2011 | 0.981 | 0.006 | 0.971 | 0.992 | 1.0 | 13995 | 8536 | |
2010 | 0.986 | 0.006 | 0.973 | 0.998 | 1.0 | 10911 | 8138 | |
2009 | 0.984 | 0.006 | 0.972 | 0.997 | 1.0 | 12041 | 7619 | |
2008 | 0.984 | 0.007 | 0.971 | 0.997 | 1.0 | 12117 | 8265 | |
2007 | 0.985 | 0.007 | 0.973 | 0.998 | 1.0 | 11081 | 8287 | |
2006 | 0.985 | 0.006 | 0.972 | 0.998 | 1.0 | 8021 | 7397 | |
2005 | 0.981 | 0.006 | 0.968 | 0.994 | 1.0 | 10740 | 8300 | |
2004 | 0.981 | 0.007 | 0.968 | 0.994 | 1.0 | 10144 | 8388 | |
2003 | 0.980 | 0.006 | 0.967 | 0.993 | 1.0 | 12774 | 8366 | |
2002 | 0.982 | 0.006 | 0.970 | 0.995 | 1.0 | 11710 | 8077 |
Parameter | Year | Estimate | Est.Error | l-95% CI | u-95% CI | Rhat | Bulk_ESS | Tail_ESS |
Intercept | 2018 | -0.316 | 0.019 | -0.353 | -0.277 | 1.0 | 14006 | 10228 |
2017 | -0.291 | 0.019 | -0.329 | -0.253 | 1.0 | 13073 | 10321 | |
2016 | -0.306 | 0.019 | -0.344 | -0.268 | 1.0 | 14068 | 10370 | |
2015 | -0.313 | 0.020 | -0.353 | -0.274 | 1.0 | 13763 | 10488 | |
2014 | -0.297 | 0.020 | -0.335 | -0.258 | 1.0 | 14018 | 10053 | |
2013 | -0.312 | 0.020 | -0.351 | -0.272 | 1.0 | 15651 | 10085 | |
2012 | -0.334 | 0.020 | -0.374 | -0.294 | 1.0 | 15044 | 9419 | |
2011 | -0.329 | 0.020 | -0.368 | -0.288 | 1.0 | 15264 | 10032 | |
2010 | -0.293 | 0.023 | -0.338 | -0.250 | 1.0 | 15413 | 10151 | |
2009 | -0.322 | 0.023 | -0.368 | -0.276 | 1.0 | 15612 | 10143 | |
2008 | -0.286 | 0.023 | -0.332 | -0.242 | 1.0 | 14927 | 10486 | |
2007 | -0.234 | 0.022 | -0.278 | -0.192 | 1.0 | 14104 | 10340 | |
2006 | -0.300 | 0.023 | -0.344 | -0.255 | 1.0 | 14512 | 9458 | |
2005 | -0.304 | 0.023 | -0.350 | -0.258 | 1.0 | 18269 | 9269 | |
2004 | -0.337 | 0.023 | -0.383 | -0.291 | 1.0 | 16123 | 9961 | |
2003 | -0.300 | 0.023 | -0.345 | -0.255 | 1.0 | 14964 | 10083 | |
2002 | -0.237 | 0.022 | -0.280 | -0.193 | 1.0 | 15569 | 9592 | |
dollars | 2018 | 0.033 | 0.002 | 0.029 | 0.037 | 1.0 | 19127 | 9998 |
2017 | 0.027 | 0.002 | 0.024 | 0.031 | 1.0 | 18387 | 10060 | |
2016 | 0.030 | 0.002 | 0.026 | 0.034 | 1.0 | 19864 | 10204 | |
2015 | 0.034 | 0.002 | 0.029 | 0.038 | 1.0 | 20147 | 10087 | |
2014 | 0.031 | 0.002 | 0.027 | 0.035 | 1.0 | 20813 | 9558 | |
2013 | 0.029 | 0.002 | 0.025 | 0.033 | 1.0 | 20564 | 9776 | |
2012 | 0.035 | 0.002 | 0.031 | 0.040 | 1.0 | 19263 | 9816 | |
2011 | 0.035 | 0.002 | 0.030 | 0.039 | 1.0 | 18440 | 9290 | |
2010 | 0.030 | 0.002 | 0.025 | 0.034 | 1.0 | 19683 | 10210 | |
2009 | 0.034 | 0.003 | 0.029 | 0.039 | 1.0 | 19411 | 10133 | |
2008 | 0.032 | 0.002 | 0.027 | 0.037 | 1.0 | 19275 | 10239 | |
2007 | 0.025 | 0.002 | 0.021 | 0.030 | 1.0 | 20606 | 9870 | |
2006 | 0.040 | 0.003 | 0.034 | 0.045 | 1.0 | 20396 | 10117 | |
2005 | 0.040 | 0.003 | 0.034 | 0.046 | 1.0 | 22024 | 9664 | |
2004 | 0.048 | 0.003 | 0.041 | 0.054 | 1.0 | 19019 | 9389 | |
2003 | 0.046 | 0.003 | 0.039 | 0.052 | 1.0 | 17897 | 9692 | |
2002 | 0.033 | 0.003 | 0.027 | 0.039 | 1.0 | 19647 | 9792 | |
grad | 2018 | 0.103 | 0.019 | 0.066 | 0.140 | 1.0 | 11657 | 8807 |
2017 | 0.108 | 0.019 | 0.071 | 0.145 | 1.0 | 10077 | 8584 | |
2016 | 0.098 | 0.019 | 0.061 | 0.136 | 1.0 | 9644 | 8660 | |
2015 | 0.086 | 0.020 | 0.048 | 0.124 | 1.0 | 11031 | 8890 | |
2014 | 0.068 | 0.020 | 0.029 | 0.105 | 1.0 | 11203 | 8900 | |
2013 | 0.097 | 0.020 | 0.058 | 0.136 | 1.0 | 12095 | 8973 | |
2012 | 0.078 | 0.020 | 0.039 | 0.118 | 1.0 | 10996 | 9294 | |
2011 | 0.079 | 0.020 | 0.039 | 0.119 | 1.0 | 12104 | 8737 | |
2010 | 0.064 | 0.023 | 0.018 | 0.110 | 1.0 | 12782 | 8831 | |
2009 | 0.064 | 0.024 | 0.017 | 0.111 | 1.0 | 12111 | 8978 | |
2008 | 0.054 | 0.025 | 0.006 | 0.103 | 1.0 | 12808 | 8695 | |
2007 | 0.067 | 0.024 | 0.020 | 0.114 | 1.0 | 10230 | 8570 | |
2006 | 0.071 | 0.024 | 0.024 | 0.118 | 1.0 | 11556 | 9107 | |
2005 | 0.096 | 0.025 | 0.047 | 0.145 | 1.0 | 15613 | 9054 | |
2004 | 0.060 | 0.025 | 0.011 | 0.108 | 1.0 | 10952 | 9517 | |
2003 | 0.027 | 0.025 | -0.022 | 0.076 | 1.0 | 11297 | 9208 | |
2002 | 0.069 | 0.025 | 0.021 | 0.118 | 1.0 | 12773 | 8684 | |
age | 2018 | 0.115 | 0.009 | 0.098 | 0.132 | 1.0 | 11227 | 9635 |
2017 | 0.106 | 0.009 | 0.090 | 0.123 | 1.0 | 11325 | 8997 | |
2016 | 0.091 | 0.009 | 0.075 | 0.108 | 1.0 | 12091 | 8374 | |
2015 | 0.082 | 0.009 | 0.064 | 0.099 | 1.0 | 10567 | 8693 | |
2014 | 0.058 | 0.009 | 0.040 | 0.076 | 1.0 | 10989 | 8467 | |
2013 | 0.056 | 0.009 | 0.038 | 0.074 | 1.0 | 12008 | 9546 | |
2012 | 0.049 | 0.009 | 0.032 | 0.067 | 1.0 | 11331 | 9625 | |
2011 | 0.050 | 0.009 | 0.032 | 0.068 | 1.0 | 13077 | 9763 | |
2010 | 0.027 | 0.010 | 0.006 | 0.047 | 1.0 | 10760 | 8808 | |
2009 | 0.047 | 0.011 | 0.026 | 0.068 | 1.0 | 10922 | 8987 | |
2008 | 0.041 | 0.011 | 0.021 | 0.062 | 1.0 | 12210 | 9086 | |
2007 | 0.048 | 0.011 | 0.028 | 0.068 | 1.0 | 12197 | 10017 | |
2006 | 0.054 | 0.010 | 0.033 | 0.074 | 1.0 | 11566 | 9238 | |
2005 | 0.059 | 0.011 | 0.038 | 0.080 | 1.0 | 14325 | 9516 | |
2004 | 0.066 | 0.011 | 0.045 | 0.087 | 1.0 | 11391 | 9310 | |
2003 | 0.043 | 0.011 | 0.022 | 0.064 | 1.0 | 12258 | 9349 | |
2002 | 0.045 | 0.011 | 0.024 | 0.066 | 1.0 | 11233 | 8473 | |
age_sq | 2018 | -0.001 | 0.008 | -0.017 | 0.015 | 1.0 | 11109 | 8882 |
2017 | 0.010 | 0.008 | -0.006 | 0.026 | 1.0 | 10722 | 8526 | |
2016 | 0.010 | 0.008 | -0.006 | 0.026 | 1.0 | 10926 | 8888 | |
2015 | 0.002 | 0.008 | -0.014 | 0.018 | 1.0 | 10702 | 8938 | |
2014 | 0.018 | 0.008 | 0.002 | 0.034 | 1.0 | 10944 | 8950 | |
2013 | 0.026 | 0.008 | 0.009 | 0.042 | 1.0 | 11501 | 9677 | |
2012 | 0.014 | 0.008 | -0.003 | 0.030 | 1.0 | 11191 | 8770 | |
2011 | 0.025 | 0.008 | 0.009 | 0.041 | 1.0 | 12111 | 9170 | |
2010 | 0.011 | 0.009 | -0.007 | 0.029 | 1.0 | 11752 | 9509 | |
2009 | 0.016 | 0.009 | -0.003 | 0.034 | 1.0 | 11600 | 9348 | |
2008 | 0.012 | 0.010 | -0.008 | 0.030 | 1.0 | 11560 | 9064 | |
2007 | -0.002 | 0.010 | -0.021 | 0.017 | 1.0 | 10630 | 8049 | |
2006 | -0.000 | 0.009 | -0.018 | 0.018 | 1.0 | 11386 | 8843 | |
2005 | 0.008 | 0.009 | -0.010 | 0.026 | 1.0 | 14429 | 8527 | |
2004 | 0.009 | 0.009 | -0.009 | 0.028 | 1.0 | 11468 | 9210 | |
2003 | 0.007 | 0.009 | -0.011 | 0.025 | 1.0 | 11813 | 8675 | |
2002 | -0.009 | 0.009 | -0.026 | 0.010 | 1.0 | 11330 | 9643 | |
male | 2018 | 0.171 | 0.016 | 0.138 | 0.203 | 1.0 | 12081 | 8698 |
2017 | 0.170 | 0.016 | 0.138 | 0.202 | 1.0 | 11135 | 7889 | |
2016 | 0.174 | 0.016 | 0.142 | 0.207 | 1.0 | 11233 | 8879 | |
2015 | 0.167 | 0.017 | 0.134 | 0.200 | 1.0 | 11220 | 8949 | |
2014 | 0.138 | 0.017 | 0.104 | 0.170 | 1.0 | 10685 | 9161 | |
2013 | 0.169 | 0.017 | 0.136 | 0.202 | 1.0 | 11261 | 8336 | |
2012 | 0.177 | 0.017 | 0.143 | 0.209 | 1.0 | 9968 | 8683 | |
2011 | 0.148 | 0.017 | 0.115 | 0.181 | 1.0 | 10976 | 8591 | |
2010 | 0.188 | 0.019 | 0.151 | 0.225 | 1.0 | 13088 | 9238 | |
2009 | 0.183 | 0.020 | 0.145 | 0.221 | 1.0 | 11448 | 8924 | |
2008 | 0.155 | 0.020 | 0.116 | 0.194 | 1.0 | 12673 | 9016 | |
2007 | 0.164 | 0.020 | 0.125 | 0.202 | 1.0 | 10811 | 8779 | |
2006 | 0.146 | 0.019 | 0.108 | 0.184 | 1.0 | 12257 | 8727 | |
2005 | 0.145 | 0.019 | 0.108 | 0.183 | 1.0 | 16872 | 9600 | |
2004 | 0.168 | 0.019 | 0.130 | 0.206 | 1.0 | 12085 | 9283 | |
2003 | 0.144 | 0.019 | 0.107 | 0.182 | 1.0 | 13152 | 9230 | |
2002 | 0.153 | 0.019 | 0.116 | 0.191 | 1.0 | 13412 | 9750 | |
sigma | 2018 | 0.979 | 0.006 | 0.968 | 0.991 | 1.0 | 14442 | 9369 |
2017 | 0.982 | 0.006 | 0.971 | 0.993 | 1.0 | 13014 | 8298 | |
2016 | 0.983 | 0.006 | 0.972 | 0.995 | 1.0 | 14319 | 8855 | |
2015 | 0.984 | 0.006 | 0.972 | 0.995 | 1.0 | 15810 | 8843 | |
2014 | 0.987 | 0.006 | 0.975 | 0.999 | 1.0 | 12493 | 8776 | |
2013 | 0.986 | 0.006 | 0.974 | 0.998 | 1.0 | 12853 | 9242 | |
2012 | 0.984 | 0.006 | 0.972 | 0.996 | 1.0 | 14535 | 9003 | |
2011 | 0.985 | 0.006 | 0.974 | 0.997 | 1.0 | 14082 | 9203 | |
2010 | 0.987 | 0.007 | 0.974 | 1.001 | 1.0 | 15396 | 8926 | |
2009 | 0.985 | 0.007 | 0.972 | 0.999 | 1.0 | 15378 | 9419 | |
2008 | 0.987 | 0.007 | 0.973 | 1.001 | 1.0 | 14429 | 8890 | |
2007 | 0.989 | 0.007 | 0.976 | 1.003 | 1.0 | 13405 | 9885 | |
2006 | 0.985 | 0.007 | 0.972 | 0.998 | 1.0 | 13470 | 9216 | |
2005 | 0.986 | 0.007 | 0.972 | 1.000 | 1.0 | 18106 | 9150 | |
2004 | 0.983 | 0.007 | 0.970 | 0.997 | 1.0 | 13797 | 8844 | |
2003 | 0.987 | 0.007 | 0.974 | 1.000 | 1.0 | 15662 | 8452 | |
2002 | 0.990 | 0.007 | 0.977 | 1.004 | 1.0 | 15600 | 9265 |
We tested the relationship between wealth and each wellbeing variable (happiness and satisfaction) using cubic B-spline models. A cubic B-spline was the most complex model (more degrees of freedom), and included here because it has been recently used to describe the maximum point at which wellbeing no longer increases with wealth (i.e., “satiety”, Jebb et al., 2018). Following Jebb et al (2018), we restricted the cubic B-spline model to n = 4, 5 and 6 knots and display wealth on a log scale.
The cubic B-spline models failed to reveal a complete satiety point (horizontal inflection) in satisfaction before the highest decile in any year. Also note that despite using a log scale, we do not observe a clear, regular logarithmic function with either wellbeing measure. Other researchers have argued that wealth represents a quantitative dimension subject to Weber’s Law of perception (Kahneman and Deaton, 2010). Under this view, similar proportional changes in income or wealth produce similar evaluations of satisfaction or happiness, rather than the absolute change. That is, a $100 increase in wealth will produce a greater impact on someone earning a minimum wage than someone earning many orders of magnitude of that amount. However while it is true that wealth clearly represents a quantitative dimension, the effects of wealth observed here represent cross-sectional differences in the population rather than changes experienced by an individual over time. It is not clear the extent to which Weber’s Law applies to cross-sectional or between-subject differences in quantitative dimensions such as wealth.
(Not included)
(Not included)
Jebb, A.T., Tay, L., Diener, E., Oishi, S., 2018. Happiness, income satiation and turning points around the world. Nature Human Behaviour 2, 33–38.
Kahneman, D., Deaton, A., 2010. High income improves evaluation of life but not emotional well-being. Proceedings of the national academy of sciences 107, 16489–16493.